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  <div class="section" id="introduction">
<h1>Introduction<a class="headerlink" href="#introduction" title="Permalink to this headline">¶</a></h1>
<p>The relax_dynamic calculation style dynamically relaxes an atomic
configuration for a specified number of timesteps. Upon completion, the
mean, <span class="math notranslate nohighlight">\(\langle X \rangle\)</span>, and standard deviation,
<span class="math notranslate nohighlight">\(\sigma_X\)</span>, of all thermo properties, <span class="math notranslate nohighlight">\(X\)</span>, are computed for
a specified range of times. This method is meant to measure equilibrium
properties of bulk materials, both at zero K and at various
temperatures.</p>
<div class="section" id="version-notes">
<h2>Version notes<a class="headerlink" href="#version-notes" title="Permalink to this headline">¶</a></h2>
<ul class="simple">
<li><p>2018-07-09: Notebook added.</p></li>
<li><p>2019-07-30: Description updated and small changes due to iprPy
version.</p></li>
<li><p>2020-05-22: Version 0.10 update - potentials now loaded from
database.</p></li>
<li><p>2020-09-22: Setup and parameter definition streamlined.</p></li>
</ul>
</div>
<div class="section" id="additional-dependencies">
<h2>Additional dependencies<a class="headerlink" href="#additional-dependencies" title="Permalink to this headline">¶</a></h2>
</div>
<div class="section" id="disclaimers">
<h2>Disclaimers<a class="headerlink" href="#disclaimers" title="Permalink to this headline">¶</a></h2>
<ul class="simple">
<li><p><a class="reference external" href="http://www.nist.gov/public_affairs/disclaimer.cfm">NIST
disclaimers</a></p></li>
<li><p>The calculation reports the standard deviation, <span class="math notranslate nohighlight">\(\sigma_X\)</span> of
the measured properties not the standard error of the mean,
<span class="math notranslate nohighlight">\(\sigma_{\langle X \rangle}\)</span>. The two are related to each other
according to
<span class="math notranslate nohighlight">\(\sigma_{\langle X \rangle} = \sigma_X \sqrt{\frac{C}{N}}\)</span>,
where <span class="math notranslate nohighlight">\(N\)</span> is the number of samples taken of <span class="math notranslate nohighlight">\(X\)</span>, and
<span class="math notranslate nohighlight">\(C\)</span> is a statistical inefficiency due to the autocorrelation of
the measurements with time. Obtaining a proper estimate of
<span class="math notranslate nohighlight">\(\sigma_{\langle X \rangle}\)</span> requires either estimating
<span class="math notranslate nohighlight">\(C\)</span> from the raw thermo data (not done here), or only taking
measurements sporadically to ensure the samples are independent.</p></li>
<li><p>Good (low error) results requires running large simulations for a
long time. The reasons for this are:</p>
<ul>
<li><p>Systems have to be large enough to avoid issues with fluctuations
across the periodic boundaries.</p></li>
<li><p>Runs must first let the systems equilibrate before meaningful
measurements can be taken.</p></li>
<li><p>The standard deviation, <span class="math notranslate nohighlight">\(\sigma\)</span>, of thermo properties is
proportional to the number of atoms, <span class="math notranslate nohighlight">\(N_a\)</span> as
<span class="math notranslate nohighlight">\(\sigma \propto \frac{1}{\sqrt{N_a}}\)</span>.</p></li>
<li><p>The standard error, <span class="math notranslate nohighlight">\(\sigma_x\)</span> of thermo properties is
proportional to the number of samples taken, <span class="math notranslate nohighlight">\(N\)</span> as
<span class="math notranslate nohighlight">\(\sigma_x \propto \frac{1}{\sqrt{N}}\)</span>.</p></li>
</ul>
</li>
</ul>
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  <h3><a href="../../index.html">Table of Contents</a></h3>
  <ul>
<li><a class="reference internal" href="#">Introduction</a><ul>
<li><a class="reference internal" href="#version-notes">Version notes</a></li>
<li><a class="reference internal" href="#additional-dependencies">Additional dependencies</a></li>
<li><a class="reference internal" href="#disclaimers">Disclaimers</a></li>
</ul>
</li>
</ul>

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